剪切流湍流输运的精确重整化群分析
Exact renormalization group analysis of turbulent transport by the shear flow
摘要：
采用Wilson提出并由Polchinski进一步发展的精确重整化群（RG）方法，研究了Avellaneda和Majda提出的剪切流模型，该模型是湍流速度场对被动标量扩散输运的简化模型。结果表明，这种精确的RG方法是能够恢复所有的标度制度的速度统计谱参数的变化，发现Avellaneda和Majda在他们的严格研究这个模型。这给了进一步的信心，RG方法，如果以正确的方式实现，而不是使用激烈的截断在Yakhot-Orszag的近似RG计划，并给出正确的预测随机偏微分方程（PDE）的解决方案的大规模行为。我们还导出了“大涡模拟“模型的模拟时，有限数量的小尺度从问题中消除。
英文摘要：
The exact renormalization group (RG) method initiated by Wilson and further developed by Polchinski is used to study the shear flow model proposed by Avellaneda and Majda as a simplified model for the diffusive transport of a passive scalar by a turbulent velocity field. It is shown that this exact RG method is capable of recovering all the scaling regimes as the spectral parameters of velocity statistics vary, found by Avellaneda and Majda in their rigorous study of this model. This gives further confidence that the RG method, if implemented in the right way instead of using drastic truncations as in the Yakhot-Orszag's approximate RG scheme, does give the correct prediction for the large scale behaviors of solutions of stochastic partial differential equations (PDE). We also derive the analog of the "large eddy simulation" models when a finite amount of small scales are eliminated from the problem.
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